Nonstationary molecular states which contain electronic coherences can be impulsively created and manipulated by using recently-developed ultrashort optical and X-ray pulses via photoexcitation, photoionization and Auger processes. We propose several stimulated-Raman detection schemes that can monitor the phase-sensitive electronic and nuclear dynamics. Three detection protocols of an X-ray broadband probe are compared - frequency dispersed transmission, integrated photon number change, and total pulse energy change. In addition each can be either linear or quadratic in the X-ray probe intensity. These various signals offer different gating windows into the molecular response which is described by correlation functions of electronic polarizabilities. Off-resonant and resonant signals are compared.
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